Averaged invariants in storage rings with synchrotron motion

Journal Article · 29 December 2020 · Journal of Instrumentation

DOI: https://doi.org/10.1088/1748-0221/15/12/p12032 · OSTI ID:1657473

Webb, Stephen ^[1]; Cook, Nathan ^[1]; Eldred, Jeffrey ^[2]

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1. RadiaSoft LLC, Boulder, CO (United States)
2. Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)

In an ideal accelerator, the single-particle dynamics can be decoupled into transverse motion—the betatron oscillations— and longitudinal motion—the synchrotron oscillations. Chromatic and dispersive effects introduce a coupling between these dynamics, the so-called synchro-betatron coupling. We present an analysis of the fully coupled dynamics over a single synchrotron oscillation that leads to an averaged invariant with synchro-betatron coupling in a generic lattice. Here, we apply this analysis to two problems: first, a toy lattice where the computations are analytically tractable, then a design for a rapid cycling synchrotron built using the integrable optics described by Danilov and Nagaitsev, showing that although there is fairly complex behavior over the course of a synchrotron oscillation, the Danilov-Nagaitsev invariants are nevertheless periodic with the synchrotron motion.

• Research Organization: Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)
• Sponsoring Organization: USDOE Office of Science (SC), High Energy Physics (HEP)
• Grant/Contract Number: AC02-07CH11359; SC0011340
• OSTI ID: 1657473
• Report Number(s): FERMILAB-PUB--20-281-AD; oai:inspirehep.net:1806090
• Journal Information: Journal of Instrumentation, Journal Name: Journal of Instrumentation Journal Issue: 12 Vol. 15; ISSN 1748-0221
• Publisher: Institute of Physics (IOP)Copyright Statement
• Country of Publication: United States
• Language: English